Crystallization Behaviors of Blast Furnace (BF) Slag in a Phase

Mar 7, 2016 - Blast furnace (BF) slag is the principal byproduct formed during the iron-making process, which generates a considerable amount of therm...
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Crystallization Behaviors of Blast Furnace (BF) Slag in a PhaseChange Cooling Process Bin Ding,‡ Hong Wang,*,†,‡ Xun Zhu,†,‡ Xian-Yan He,‡ Qiang Liao,†,‡ and Yu Tan‡ †

Key Laboratory of Low-grade Energy Utilization Technologies and Systems, Chongqing University, Chongqing 400030, China Institute of Engineering Thermophysics, Chongqing University, Chongqing 400030, China

‡

ABSTRACT: Blast furnace (BF) slag is the principal byproduct formed during the iron-making process, which generates a considerable amount of thermal energy. However, to simultaneously recover the maximum amount of residual heat and obtain vitreous slag using a low conduction coefficient of air is a primary challenge of the dry granulation technique, which has not been solved by either fundamental research or engineering applications. In the current study, the evolution of temperature inside molten BF slag was experimentally investigated using the directional solidification technique to calculate the local heat-transfer coefficient and the average cooling rates. Furthermore, the effects of the average cooling rate on the vitreous phase content of the BF slag during solidification were investigated based on X-ray diffraction (XRD) technology. The results indicate that the average cooling rate from the cooling side to the adiabatic side gradually decreased due to the increase in heat resistance and latent heat released. Moreover, the vitreous phase content of the BF slag at different positions decreased as the average cooling rate decreased. Conversely, the crystal phase content increased gradually and released more latent heat, which further reduced the average cooling rate. In addition, the crystal phase obtained at different positions was presented as åkermanite, and the average critical cooling rate was 10.6 °C s−1. Lastly, dimensionless correlations were developed to predict the distributions of the average cooling rate and the vitreous phase content of the BF slag along the vertical direction, and the theoretical value has a good agreement with the experimental data.

1. INTRODUCTION Blast furnace (BF) slag is the primary byproduct formed during the iron-making process with a high temperature between 1450 and 1550 °C, which indicates that it contains a large amount of residual heat that can be recovered. In 2014, China’s crude steel production reached ∼823 million tons, whereas the BF slag production was ∼274 million tons.1 Particularly, the total residual heat contained in the BF slag equaled the calorific value of 15.9 million tons of standard coal. Moreover, BF slag is primarily composed of CaO, SiO2, Al2O3, MgO, which is similar to cement.2 Previous research indicated that different cooling rates resulted in different phase transformations.3,4 A rapid cooling of the BF slag will produce a vitreous phase with high cementation activity, which can be used as the raw materials of cement.5−7 Currently, water quench technology is the most effective treatment to obtain glassy slag. However, this treatment consumes a tremendous amount of water and fails to recover the residual heat. Therefore, driven by the demand for sustainable development of industries and the environment, a technology that considers both residual heat recovery and comprehensive BF slag utilization must be developed. Thus, several dry granulation heat recovery technologies have been proposed.2 Moreover, the centrifugal granulation method was one of the most feasible technologies proposed by Pickering in 1985.8 In this technical process, the melting slag is simultaneously broken into droplets using a high-speed granulator and cooled by air. However, the air cooling rate is relatively lower than the water quenching rate and may not be sufficiently fast to achieve slag vitrification. Moreover, the cooling rate is further reduced due to the release of large amounts of latent heat during solidification. Thus, cooling air © 2016 American Chemical Society

with a high velocity is essential to obtain vitreous slag, which significantly decreases the quality and quantity of the recovered residual heat. Consequently, simultaneously obtaining the vitreous slag and recovering the maximum amount of residual heat using cooling air is a major challenge, which has impeded the popularization of the dry granulation and residual heat recovery technologies. To improve the situation, it is crucial to realize the effects of the phase-change heat-transfer characteristics on the crystallization behaviors inside the BF slag. Currently, the single hot thermocouple technique (SHTT),9−11 differential scanning calorimetry (DSC),12,13 and viscosity-temperature curve method14 are the most popular methods used to explore the crystallization behaviors of melting slag. For instance, the crystallization ratio of a synthetic coal slag under different isothermal conditions and cooling rates was investigated by Xuan et al.10 using the SHTT. Moreover, the SHTT was adapted by Klug et al.15 to obtain the critical cooling rate of artificial slag. In addition, the crystallization mechanism of the BF slag under different cooling rates using DSC was considered by Gan et al.13 The result indicated that the crystallization mechanism was regulated by both surface nucleation and one-dimensional growth with bulk nucleation. However, the previous studies primarily focused on the crystallization characteristics under different isothermal temperatures and continuous cooling rates, i.e., the heat transfer inside the slag was ignored. This result indicates that these methods could not be used to explore the effects of phase-change heatReceived: December 28, 2015 Revised: March 7, 2016 Published: March 7, 2016 3331

DOI: 10.1021/acs.energyfuels.5b03000 Energy Fuels 2016, 30, 3331−3339

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Energy & Fuels transfer characteristics on the crystallization behaviors inside the slag. Complementary to these methods, the directional solidification technique primarily focuses on the phase-change heat-transfer process of the working medium along a definite direction.16−18 For example, the evolution of the average cooling rate and the tip growth rate of the Zn−Sn alloy along the vertical direction was obtained by Santos et al.16 Moreover, Ferreira et al.17 explored the temperature distribution along the vertical direction of different alloys and the heat-transfer coefficient profiles on the cooling interface. The result indicated that the initial melt temperature distribution had a significant influence on the heat-transfer-coefficient profiles. Thus, this method was an effective approach for studying the phasechange heat-transfer characteristics of the BF slag under different cooling conditions. In addition, X-ray diffraction (XRD) was used to analyze the vitreous phase or the composition content of the working medium.19−21 For instance, the tin content distribution along the vertical direction was obtained by analyzing the XRD patterns of Zn−Sn solder alloy samples at different positions.16 Therefore, the effects of the phase-change heat-transfer characteristics on the crystallization behaviors can be obtained when the directional solidification technique was used in combination with XRD. In the current study, the coupled mechanism of the phasechange heat-transfer characteristics and the crystallization behaviors was investigated by analyzing the effects of the average cooling rate on the phase evolution of the BF slag. The DSC was adapted to detect the characteristic temperature of the BF slag, such as the liquidus temperature and the glasstransition temperature. A directional solidification technique and XRD were used to obtain the distribution of the average cooling rate and vitreous phase content along the vertical direction, respectively. In addition, the evolution rule of the crystalline phase along the vertical direction was determined using scanning electron microscopy (SEM). Lastly, the dimensionless correlations of these parameters were obtained by fitting the experimental data.

Figure 1. Schematic representation of the experimental setup. Before the experiment, the BF slag contained by the graphite crucible was heated to the designated temperature (1550 °C) in a heating furnace. Meanwhile, the stainless crucible was preheated to 1100 °C using a flame spray gun. After completing the heat-treatment process, the melting BF slag was removed from the heating furnace and rapidly poured into the stainless crucible. The cooling water valve then was opened, and all of the data were recorded by the data acquisition unit. The experiment ended when the temperature at the top position decreased to 250 °C. After the directional solidification experiment, the sliced BF slag samples with a thickness of 1 mm at a position of y = 1, 4, 7, 10, 16, 22, 28, 40, and 52 mm were obtained using a diamond wire cutting machine (Model WXD-170, Mike, China). The samples were ground into powder with an average diameter of 38 μm. Then, XRD measurements were performed to determine the vitreous phase content of the samples. The XRD patterns were obtained using a Rigaku XRD-D/max-1200 system with a scanning speed of 2° min−1. Moreover, an SEM system (Model S-4800, Hitachi, Japan) was used to analyze the microstructural characteristics of the BF slag samples. 2.2. Working Medium. In the current study, BF slag from Chongqing Iron & Steel (Group) Co., Ltd. (China) was used as the working medium. Prior to the experiments, the chemical composition and its mass percentage were analyzed using an X-ray fluorescence (XRF) spectrometer (Model XRF-1800, Shimadzu, Japan), as listed in Table 1. The table indicates that the key components of the working medium were CaO, SiO2, Al2O3, and MgO, and the total mass percentage was 88.89%. The basicity [(C + M) × (S + A)−1] = [(CaO + MgO) × (SiO2 + Al2O3)−1] of the testing BF slag was 1.13, thus indicating an alkaline slag.22,23 Moreover, the liquidus temperature and the glass-transition temperature of the vitreous phase slag was detected by differential scanning calorimetry (DSC) (Q20 DSC, TA, USA), as displayed in Figure 2. It can be seen that the liquidus temperature and the glass-transition temperature of the working medium were 1350 and 740 °C, respectively. In addition, the physical properties of the working medium are listed in Table 2. As indicated in Table 2, the values of the density and heat capacity of the BF slag in the solid and liquid phases were similar. However, the value of the thermal conductivity in the liquid phase was only 16.7% of that in the solid phase. Moreover, the latent heat released by the vitreous phase slag was only 62.3% of that released by crystal phase slag of the same quality. 2.3. Data Processing and Error Analysis. Based on the current research,26,27 the instantaneous heat flux (qi) from the interface

2. EXPERIMENTAL PROCEDURE 2.1. Experimental System and Method. The experimental setup for the directional solidification of the BF slag, as indicated in Figure 1, consisted of a cooling system, test unit, and measurement system. In the cooling system, spray cooling was performed using water as the coolant to remove the heat from the bottom of the test unit, and the flow rate was adjustable. In the test unit, a stainless crucible with a length of 100 mm and a diameter of 36 mm was manufactured as a chamber to contain the molten BF slag. At the bottom of the chamber, a stainless steel slice with a thickness of 5 mm was used to seal the crucible and as a heat exchanger plate. Moreover, the stainless crucible was covered with a layer of insulating alumina to minimize heat loss. Thus, the heat-transfer process was approximately considered as onedimensional heat transfer, and the direction of heat transfer was in a reverse direction from that of the solidification. The maximum heat loss of the overall experimental system was 2%. The measurement system was comprised of thermocouples, a data acquisition unit (Keithley Instruments, Model 2701), and a computer. Ten type B thermocouples (diameter of ϕ = 0.5 mm) were positioned at 1, 4, 7, 10, 16, 22, 28, 34, 40, and 52 mm from the bottom of the BF slag. Moreover, two type K thermocouples (ϕ = 1 mm) were inserted into the center of the heat exchanger plate to obtain the temperature near the top and bottom of the heat exchanger plate. Moreover, the distance between the two type K thermocouples was 3 mm, with an accuracy of ±0.02 mm. Moreover, all the thermocouples were calibrated in advance, with an accuracy of ±0.1 °C. 3332

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top and bottom of the stainless steel slice, respectively; and δ is the spacing between the two thermocouples. The average heat-transfer coefficient at the interface between the stainless steel slice and the BF slag can be calculated as follows:

Table 1. Chemical Composition of the Tested BF Slag oxide

composition (wt %)

CaO SiO2 Al2O3 MgO TiO2 SO3 MnO BaO K2O Fe2O3 SrO Na2O Cr2O3 ZrO2

39.20 30.34 11.32 8.03 5.96 2.52 0.80 0.60 0.44 0.33 0.17 0.17 0.07 0.05

h=

1 n

n

∑ i=0

qi Ti − Tti

(2)

where Ti is the temperature of the BF slag near the cooling interface (y = 1 mm) at t = ti; and n is the total time steps during the experiments. Moreover, the average cooling rate of the BF slag during solidification can be obtained as follows: v=

Tl − Tg ts

(3)

where Tl is the liquidus temperature of the BF slag, Tg is the glasstransition temperature, and ts is the total time of the BF slag cooled from Tl to Tg. In addition, the XRD method was used to quantify the vitreous phase content in different sliced BF slag samples. Furthermore, the correlation28 can be expressed as follows: β=

Ig Ig + KIc

(4)

where Ig is the integral area of the vitreous phase, Ic the integral area of the crystal phase, and K the noncrystalline quotient of the BF slag. Moreover, the integral area is 2θ = 20°−40°, and the value of K in this report is 1.7, which has been previously obtained. In addition, the previous study28 has a full description of the process for obtaining the value of K. The estimated experimental error in the measurement of qi in eq 1 is the sum of Tt, Tb, and δ, which can be expressed as follows: Δqi qi

Table 2. Physical Properties of the Working Medium parameter

nomenclature

2.84 g cm−3 (ref 24) 2.75 g cm−3 (ref 24)

cps cpl

1.15 J g−1 °C 1.30 J g−1 °C

λs λl

0.90 W m−1 K−1 (ref 24) 0.15 W m−1 K−1 (ref 24)

Lc Lv Tl Tg

456 J g−1 284 J g−1 1350 °C 740 °C

−1 −1

(ref 25) (ref 25)

between the stainless steel slice and the BF slag at a certain time ti can be expressed as follows:

⎛ T − Tbi ⎞ ⎟ qi = λ⎜ ti ⎝ δ ⎠

2

+

ΔTb Tb

2

+

Δδ δ

2

(5)

3. RESULTS AND DISCUSSION 3.1. Phase-Change Heat-Transfer Characteristics of BF Slag. The previous research29 indicated that the latent heat of the vitreous phase was released evenly at a temperature between the glass-transition temperature and the liquidus temperature. Conversely, the latent heat released by the crystal phase slag occurred in a narrow temperature range, and its value was considerably larger. Thus, the latent heat released by the crystal phase has a pronounced effect on the solidification of the BF slag. To explore the phase-change heat-transfer characteristics of the BF slag, the temperature distribution along the vertical direction during the solidification of the BF slag is illustrated in Figure 3, where the flow rate of the cooling water was set at 160 L h−1. For simplicity, the total length of the BF slag in the stainless crucible is represented by Y, and the relative position along the vertical direction is represented by y. As indicated in Figure 3, the temperature near the cooling interface (y = 1 mm) decreased more rapidly, compared to that of other positions, indicating that the capacity of spray cooling can easily remove the sensible and latent heat from the molten slag. Moreover, from y = 10 mm to y = 52 mm, the temperature curve gradually became flatter in the temperature range between 1210 °C and 1350 °C. When the temperature reached different values below 1210 °C, the curve dropped rapidly with

value

ρs ρl

ΔTt Tt

The fractional uncertainty in the measurements of Tt, Tb, and δ has been mentioned previously; hence, the largest uncertainty of qi is 0.7%. Furthermore, the largest uncertainty of h is 0.8%. Similarly, the uncertainties of v and β are 0.5% and 1%, respectively.

Figure 2. Typical differential scanning calorimetry (DSC) pattern of the vitreous phase slag.

density in the solid zone in the liquid zone heat capacity in the solid zone in the liquid zone thermal conductivity in the solid zone in the liquid zone latent heat crystal phase vitreous phase liquidus temperature glass-transition temperature

=

(1)

where λ is the thermal conductivity of the stainless steel slice; subscript i represents the time step of ti; Tt and Tb are the temperatures near the 3333

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rapid increase in the thermal resistance and latent heat. The parameters in Table 2 and Figure 5b indicated that, from y = 1 mm to y = 10 mm, the thermal resistance and latent heat increased by 762% and 36.4%, respectively. The average cooling rate then gradually decreased to 2.2 °C s−1 (y = 52 mm), because the thermal resistance and latent heat slightly increased along the vertical direction. In addition, the increased value of the thermal resistance and latent heat was 414% and 4.4%, respectively. Moreover, the effects of the total length of the BF slag on the average cooling rate distribution along the vertical direction was considered. Thus, the average cooling rate distribution for different total lengths (Y = 16, 28, and 52 mm) along the vertical direction is illustrated in Figure 4b. The figure indicates that the average cooling rate at the same position increased with a decrease in the overall length. For example, for the case of Y = 28 and 16 mm, the average cooling rate at a position of y = 1 mm increased to 24.1 and 26.1 °C s−1, respectively. This result was attributed to the total heat of the BF slag decreasing as the total length decreases. Furthermore, BF slag cooled at a slower cooling rate will release more latent heat, which will further decrease the average cooling rate. Thus, the difference in the average cooling rate between the case of Y = 52 mm and Y = 16 mm increased along the vertical direction. For example, the value of the difference at a position of y = 1 and 4 mm was 5.1 and 8.1 °C s−1, respectively. Moreover, as the thermal resistance increased along the vertical direction, the effects of the thermal resistance on the average cooling rate were enhanced. Thus, the gap of the average cooling rate narrowed along the vertical direction after y > 4 mm. For example, the value of the difference decreased to 0.8 °C s−1 at a position of y = 16 mm. 3.2. Crystallization Behaviors of BF Slag. During the solidification of the BF slag, the crystal and vitreous phases will precipitate, because of the various cooling rates. To identify the phase evolution along the vertical direction, the samples (Y = 52 mm, Q = 160 L h−1) at different positions were examined using the XRD technique. Furthermore, the XRD results of the samples at y = 1, 4, 7, and 52 mm are illustrated in Figure 5a. It can be seen that all of the resulting diffraction patterns indicate the same general trend, i.e., the crystal phase obtained at different positions is presented as åkermanite. Moreover, the intensity and quantity of the crystallization peak increased along the vertical direction. Furthermore, the value of the

Figure 3. Temperature distribution along the vertical direction.

the same trend. This result indicated that the crystal phase precipitated in the temperature range of 1210−1350 °C, and the crystal phase content increased along the vertical direction. Therefore, because of the thermal resistance and the released latent heat increasing along the vertical direction, the temperature curve became flatter. As mentioned in the previous study,24 the melting BF slag will not crystallize immediately when the temperature is below the liquidus temperature (Tl). An incubation period exists for nucleation, and the nucleation process is dominantly controlled by the cooling rate. Thus, the BF slag will not precipitate the crystal phase when the temperature drops below the glasstransition temperature (Tg) during the incubation period. Similarly, the pure crystallization slag can be obtained when the cooling rate is sufficiently slow. Thus, the content of the crystal phase and the cooling rate between Tg and Tl was interactional. However, the cooling rate of the BF slag was inconsistent, because of the effects of released latent heat and varying thermal resistance. Therefore, the cooling condition of the BF slag can be clearly represented at different positions effectively. To address this problem, an average cooling rate was calculated using eq 3, as depicted in Figure 4a. The figure indicates that the average cooling rate decreased rapidly near the cooling surface. For instance, at a position of y = 1 mm, the average cooling rate was 20.9 °C s−1, which then decreased to 5.2 °C s−1 at a position of y = 10 mm. This result was attributed to the

Figure 4. Average cooling rate distribution along the vertical direction. 3334

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Figure 5. (a) XRD patterns of the samples at different positions; (b) vitreous content distribution along the vertical direction.

vitreous phase content at different positions was determined using eq 4, as indicated in Figure 5b. It can be observed from Figure 5b that the distribution of the vitreous content was similar to the distribution of the average cooling rate. The figure indicates that the full vitreous phase formed at a position of y = 1 mm. Then, at a position of y = 10 mm, the vitreous phase content (β) rapidly decreased to 43.8%. Eventually, the value slowly decreased to 32.7% at a position of y = 52 mm. As noted above, as the average cooling rate decreased along the vertical direction, the crystallization temperature and growth time of the crystal phase increased gradually. Furthermore, the viscosity of the melting BF slag decreased as the temperature increased,30 thus indicating that the growth resistance of the crystal phase decreased along the vertical direction. Hence, the growth rate and time of the crystal phase increased along the vertical direction. Moreover, with an increase in the crystal phase content (1 − β > 50%), the growth rate of the crystal phase decreased. Furthermore, when the content of the crystal phase increased along the vertical direction, the released latent heat increased gradually, which further increased the growth rate and time of the crystal phase. Thus, the distribution of the vitreous phase content was similar to that of the average cooling rate. To realize the microstructure evolution of the BF slag along the vertical direction, the SEM images at the positions of y = 1, 4, 7, and 52 mm were tested, as indicated in Figure 6. This figure indicates that the crystal phase can hardly be observed in Figure 6a. The precipitated crystal phase then appeared in the shape of the plate in Figures 6b and 6c. The crystal phase in Figure 6d then transformed to the shape of a short columnar or plate. In addition, the SEM images indicated that the content of the vitreous phase increased along the vertical direction, which agreed well with the XRD results. 3.3. Effects of the Cooling Condition on the Solidification Characteristics of BF Slag. To explore the effects of the cooling condition on the average cooling rate distribution and vitreous phase evolution along the vertical direction, the total length of BF slag was set as Y = 52 mm, and the cooling water flow rate was set at Q = 10, 25, 80, and 160 L h−1. To clearly evaluate the cooling condition, the average heat-transfer coefficient (h) at the cooling surface between the BF slag and the heat exchange plate was calculated using eqs 1 and 2. A distribution of the average heat-transfer coefficient under different cooling water flow rates is indicated in Figure 7. This figure indicates that the average heat-transfer coefficient improved linearly by increasing the cooling water flow rate.

Figure 6. SEM images of the samples at different positions.

Moreover, its value at the cooling conditions of Q = 10 and 160 L h−1 was 293 and 897 W m−2 K−1, respectively. This result will be conducive to a significant change in the scale of the average cooling rate and the vitreous phase content. The effects of the average heat-transfer coefficient on the average cooling rate of the BF slag at the same position is indicated in Figure 8. Figure 8 indicates that the average cooling rate of the BF slag increased gradually as the average heat-transfer coefficient improved. Moreover, the effects of the average heat-transfer coefficient on the average cooling rate weakened when h > 516 W m−2 K−1. 3335

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was under the control of the cooling conditions. Moreover, the average cooling rate near the adiabatic interface was governed by the thermal resistance. Moreover, the effects of the cooling conditions on the vitreous phase evolution was explored by analyzing the XRD patterns. The XRD patterns of the samples under different cooling conditions are described in Figure 9. The samples in Figures 9a, 9b, and 9c were obtained from the positions of y = 1, 7, and 52 mm, respectively. Moreover, the vitreous phase content of the samples under the different cooling conditions and positions was determined, as indicated in Figure 9d. It can be seen that the crystal phase can barely be observed at a position of y = 1 mm under the different cooling conditions. As the BF slag solidified along the vertical direction, the distribution rule of the vitreous phase content was similar to that of the average cooling rate. For example, at a position of y = 7 mm, the vitreous phase content increased from 35% to 65% when the average heat-transfer coefficient gradually increased. Moreover, at a position of y = 52 mm, the value slowly increased from 30% to 32.6%. This result can be ascribed to the interaction between the average cooling rate and the vitreous phase content. 3.4. Effects of the Average Cooling Rate on the Vitreous Phase Content of BF Slag. To explore the relationship between the average cooling rate and the vitreous phase content of the BF slag, the vitreous phase content was obtained under different average cooling rates, as indicated in Figure 10. This figure indicated that the crystal phase crystallized out from the slag gradually when the average cooling rate was 85% can be used for cement productions. Hence, an average cooling rate of >7.8 °C s−1 could easily meet these requirements. Moreover, in the dry granulation and waste heat recovery system, a smaller average cooling rate was beneficial for recovering more residual heat and saving draft fan power. Thus, when considering the utilization and heat recovery of the BF slag, an average cooling rate of v = 7.8 °C s−1 was considered to be appropriate and economical. 3.5. Theoretical Analysis of the Solidification Process. As previously mentioned, the distribution of the average cooling rate along the vertical direction was controlled by the overall length and cooling conditions. To predict the distribution of the average cooling rate along the vertical direction, the overall length, cooling condition, position and average cooling rate can be transformed to dimensionless forms as follows:

Figure 7. Distribution of the average heat-transfer coefficient under different cooling water flow rates.

Figure 8. Effects of the average heat-transfer coefficient on the average cooling rate.

For instance, at a position of y = 1 mm, the average cooling rate increased from 8.3 °C s−1 to 18.9 °C s−1 when the average heattransfer coefficient improved from 293 W m−2 K−1 to 516 W m−2 K−1. However, the average cooling rate only increased to 20.9 °C s−1 at the cooling condition of h = 897 W m−2 K−1. As previously mentioned, the thermal resistance near the cooling surface was extremely small. Thus, this result can be attributed to the combined influence of the average heat-transfer coefficient and the conduction heat-transfer mechanism. Furthermore, the heat released by the BF slag could not be removed by the cooling water in a timely manner when h < 516 W m−2 K−1. When the value of h increased (h > 516 W m−2 K−1), the average cooling rate was limited by the ability of the releasing heat, which was evaluated by the thermal diffusion coefficient. In addition, the influence of the average heattransfer coefficient on the average cooling rate weakened along the vertical direction. Furthermore, Figure 8 suggested that the average cooling rate at a position of y = 1 mm increased a total of 152% when the average heat-transfer coefficient increased. However, at a position of y = 52 mm, its value reduced to 77%. This result was ascribed to the sharply increased thermal resistance along the vertical direction, i.e., the cooling rate was confined by the larger thermal resistance. In conclusion, the average cooling rate of the BF slag near the cooling interface 3336

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Figure 9. (a−c) XRD patterns of the samples under different cooling conditions (at positions of (a) y = 1 mm, (b) y = 7 mm, and (c) y = 52 mm); (d) vitreous phase content distribution under different cooling conditions.

v* =

v vc

(9)

where C = 1 mm is the unit length of the BF slag; λ = 0.71 W m−1 K−1 is the average thermal conductivity of the BF slag during solidification; and vc is the critical average cooling rate of the BF slag. Thus, considering the introduced dimensionless parameters, the correlation of the average cooling rate distribution can be obtained by fitting the experimental data as follows: v* = 3.36(Y *)−0.72 Φ0.69(y∗)−0.55

The correlation is available for 1 < Y* < 52, 0.4 < Φ < 1.3, and 0.02 < y* < 1. The deviation between the fitting results and the experimental data is illustrated in Figure 11a. The prediction of the current correlation indicates a good agreement between the prediction and the experimental data with a variance (R2) of 0.98. Moreover, based on the Johnson−Mehl−Avrami (JMA) equation, which was used to calculate the isothermal kinetics of crystallization,10,13 the modified correlation between the dimensionless average cooling rate (v*) and the vitreous phase content (β) was obtained by fitting the experimental data. Considering the various influencing factors of the crystallization characteristics in different stages, the correlation can be expressed as follows:

Figure 10. Vitreous content distribution at different average cooling rates.

Y* =

Y C

(6)

Φ=

hC λ

(7)

y* =

y Y

(8)

(10)

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Figure 11. (a) Divergence of the dimensionless average cooling rate (v*) between the experimental data and the correlation; (b) divergence of the vitreous phase content (β) between the experimental data and the correlation.

⎧1 (for v* ≥ 1) ⎪ ⎪ 9.47 − 15.48v * β = ⎨1 − e (for 0.68 ≤ v* < 1) ⎪ ⎪ 0.27 + e 4.43v * −3.96 (for 0.12 < v* < 0.68) ⎩

■

AUTHOR INFORMATION

Corresponding Author

*Tel.: +86-023-65102474. E-mail: [email protected]. (11)

Notes

The authors declare no competing financial interest.

Thus, the correlation is available for v* > 0.12, and the divergence between the fitting result and the experimental data is exhibited in Figure 11b. Figure 11b indicates that the correlation fits the experimental data well, and the variance (R2) in stages I and II was 1.0 and 0.99, respectively.

■

ACKNOWLEDGMENTS

■

REFERENCES

The authors gratefully acknowledge financial support from the National Basic Research Program of China (973 Program) (No. 2012CB720403).

4. CONCLUSIONS In the current study, the evolution of the temperature inside the molten BF slag was experimentally investigated using the directional solidification technique to calculate the average heat-transfer coefficient (h) and the average cooling rates (v). Furthermore, the effects of the average cooling rate on the vitreous phase content of the BF slag during solidification were investigated based on the X-ray diffraction (XRD) technology. Moreover, the evolution rule of the crystal phase along the vertical direction was examined using scanning electron microscopy (SEM). In addition, the dimensionless correlations of these parameters, such as the average cooling rate, vitreous phase content, average heat-transfer coefficient, and overall length of BF slag, were determined. The primary conclusions are as follows: (1) The growth rate of the vitreous phase is determined by the cooling rate. When y > 10 mm, the curve of the cooling rate becomes flat, because of the heat-transfer process being dominantly controlled by the internal heat conduction with an increase in both the thermal resistance and the released latent heat. In addition, the crystal phase obtained at the different positions can be presented as åkermanite. (2) The critical average cooling rate was 10.6 °C s−1; furthermore, considering the heat recovery efficiency and the vitreous phase content of BF slag, v = 7.8 °C s−1 was an appropriate and economical average cooling rate. (3) The dimensionless correlations based on the experimental data were developed to predict the distribution of the average cooling rate and the vitreous phase content in the range of Φ = 0.4−1.3.

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DOI: 10.1021/acs.energyfuels.5b03000 Energy Fuels 2016, 30, 3331−3339